75.2.6 problem 26

Internal problem ID [16683]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 2. The method of isoclines. Exercises page 27
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 09:17:55 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\left (y-1\right ) x \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(diff(y(x),x)=(y(x)-1)*x,y(x), singsol=all)
 

\[ y = 1+{\mathrm e}^{\frac {x^{2}}{2}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 24

DSolve[D[y[x],x]==(y[x]-1)*x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 1+c_1 e^{\frac {x^2}{2}} \\ y(x)\to 1 \\ \end{align*}